Periodic Reporting for period 2 - ConsQuanDyn (Constrained Quantum Dynamics)
Berichtszeitraum: 2022-04-01 bis 2023-09-30
Recent conceptional and technical progress makes it possible to experimentally prepare and explore strongly-correlated, non-equilibrium quantum states of matter. This progress creates an exciting and interdisciplinary research field that bridges condensed matter, quantum information and atomic physics. The general intuition is that non-equilibrium quantum states relax at late times to their thermal equilibrium following the laws of hydrodynamics. However, the collective response of interacting quantum matter brought far from their thermal equilibrium can also lead to much more spectacular phenomena, including non-trivial relaxation dynamics via prethermal states, dynamical quantum phases that do not even exist in equilibrium, and dynamical phase transitions between these emergent phases. Understanding emergent dynamical properties of interacting quantum matter is hence of central importance both conceptually as well as for interpreting and devising experiments.
Strong interactions and frustration often lead to dynamically constrained excitations of quantum matter. Examples include spin-ice compounds whose spin moments are aligned to fulfil a local ice rule of two spins pointing in and two spins pointing out, frustrated quantum magnets with dimerized excitations, and fracton phases with excitations that are only mobile in certain directions if at all. Recent experiments with synthetic quantum matter has started to explore systems with constrained excitations. While the equilibrium properties of constrained quantum systems have been intensely studied over the last decades, it remains an open challenge to understand their far-from-equilibrium quantum dynamics and the dynamical phases they realize. The central focus of the project ConsQuanDyn is to develop new concepts and new theoretical methods to study constrained quantum systems far from thermal equilibrium.
The project has three principal objectives each of which would represent a major contribution to the field:
(O1) To identify glassy dynamics and hydrodynamic transport in constrained quantum lattice gas, quantum dimer and fracton models.
(O2) To demonstrate information scrambling and entanglement growth in constrained Hilbert spaces.
(O3) To predict exotic dynamical quantum phases and to study their dynamical criticality both in quenched and in periodically driven constrained systems.
To successfully meet our ambitious objectives, we will develop two complementary theoretical approaches based on exact numerical techniques and on non-equilibrium field theory. This allows us to understand fundamental dynamical properties of constrained quantum systems and to guide future experiments. Constrained quantum systems may realize topological quantum bits and self-correcting quantum memories. Due to the international effort of inventing new quantum technology, that inherently operates out of equilibrium, it is now the right time to foster a deep understanding of the non-equilibrium dynamics in constrained quantum matter, which is the central goal of the project ConsQuanDyn.
Strong interactions and frustration often lead to dynamically constrained excitations of quantum matter. Examples include spin-ice compounds whose spin moments are aligned to fulfil a local ice rule of two spins pointing in and two spins pointing out, frustrated quantum magnets with dimerized excitations, and fracton phases with excitations that are only mobile in certain directions if at all. Recent experiments with synthetic quantum matter has started to explore systems with constrained excitations. While the equilibrium properties of constrained quantum systems have been intensely studied over the last decades, it remains an open challenge to understand their far-from-equilibrium quantum dynamics and the dynamical phases they realize. The central focus of the project ConsQuanDyn is to develop new concepts and new theoretical methods to study constrained quantum systems far from thermal equilibrium.
The project has three principal objectives each of which would represent a major contribution to the field:
(O1) To identify glassy dynamics and hydrodynamic transport in constrained quantum lattice gas, quantum dimer and fracton models.
(O2) To demonstrate information scrambling and entanglement growth in constrained Hilbert spaces.
(O3) To predict exotic dynamical quantum phases and to study their dynamical criticality both in quenched and in periodically driven constrained systems.
To successfully meet our ambitious objectives, we will develop two complementary theoretical approaches based on exact numerical techniques and on non-equilibrium field theory. This allows us to understand fundamental dynamical properties of constrained quantum systems and to guide future experiments. Constrained quantum systems may realize topological quantum bits and self-correcting quantum memories. Due to the international effort of inventing new quantum technology, that inherently operates out of equilibrium, it is now the right time to foster a deep understanding of the non-equilibrium dynamics in constrained quantum matter, which is the central goal of the project ConsQuanDyn.
The research of the project ConsQuanDyn focuses on the far-from-equilibrium quantum dynamics of strongly correlated many-body systems with constraints that arise from geometric frustration and strong interactions. Our research in the past reporting period has focused on the three central objectives and we made important progress on all of them:
(a) Constrained hydrodynamic transport
Identifying universal properties of non-equilibrium quantum states is a major challenge in modern physics. A fascinating prediction is that classical hydrodynamics of a few conserved quantities emerges universally in the evolution of any complex quantum system, as strong interactions entangle and effectively mix local degrees of freedom. In this project, we studied how constraints can modify transport. For example, we investigated fractonic quantum matter in which the total charge and in addition the total dipole moment are conserved. We found that ergodic systems with these constraints can escape the conventional scenario of diffusive transport, and display subdiffusive decay instead. This unconventional transport has also been experimentally explored in quantum simulators of ultracold atoms subjected to a tilted optical lattice. The type of transport, depends however, on the structure of the underlying systems. Systems with kinetic constraints, as they occur in quantum glasses, can also exhibit subdiffusive transport. The mechanism behind it, is rather distinct from the one of fractonic systems and is based on tracer diffusion, that is diffusion of a tagged particle with infinitely repulsive interactions.
(b) Information scrambling and operator growth in constrained spaces
The far-from-equilibrium dynamics of generic interacting quantum systems is characterized by a handful of universal guiding principles, among them the ballistic spreading of initially local operators. We have shown, that in certain constrained many-body systems the structure of conservation laws can cause a drastic modification of this universal behavior. As an example, we studied operator growth characterized by out-of-time-order correlations (OTOCs) in a dipole-conserving fracton system. We have identified a critical point with sub-ballistically moving OTOC front, that separates a ballistic from a dynamically frozen phase of operator growth. This critical point is tied to an underlying localization transition and we use its associated scaling properties to derive an effective description of the moving operator front via a biased random walk with long waiting times.
(c) Characterizing exotic phases with constraints
Many-body systems with gauge constraints can lead to unconventional phases of matter with topological order. An example are quantum spin liquids. We have developed a quantum algorithm to realize such states on a superconducting quantum information processor, and have simulated anyon braiding and shown how to measure the topological entanglement entropy of the wave function. We furthermore developed experimental probes of topological phases of matter based on spin-polarized scanning-tunneling microscopy, nitrogen-vacancy center magnetometry, or angle-resolved photoemission spectroscopy. We, moreover, investigated periodically driven quantum spin liquids that are subjected to gauge constraints and identified an unconventional dynamical regime, which cannot be described by a single effective Hamiltonian even in the limit of high driving frequency. The reason for this apparent counter-intuitive behavior is that fractional excitations typically couple asymmetrically to the drive.
With the project ConsQuanDyn, we could shed light on several dynamical phenomena that arise from constraints in quantum many-body systems.
(a) Constrained hydrodynamic transport
Identifying universal properties of non-equilibrium quantum states is a major challenge in modern physics. A fascinating prediction is that classical hydrodynamics of a few conserved quantities emerges universally in the evolution of any complex quantum system, as strong interactions entangle and effectively mix local degrees of freedom. In this project, we studied how constraints can modify transport. For example, we investigated fractonic quantum matter in which the total charge and in addition the total dipole moment are conserved. We found that ergodic systems with these constraints can escape the conventional scenario of diffusive transport, and display subdiffusive decay instead. This unconventional transport has also been experimentally explored in quantum simulators of ultracold atoms subjected to a tilted optical lattice. The type of transport, depends however, on the structure of the underlying systems. Systems with kinetic constraints, as they occur in quantum glasses, can also exhibit subdiffusive transport. The mechanism behind it, is rather distinct from the one of fractonic systems and is based on tracer diffusion, that is diffusion of a tagged particle with infinitely repulsive interactions.
(b) Information scrambling and operator growth in constrained spaces
The far-from-equilibrium dynamics of generic interacting quantum systems is characterized by a handful of universal guiding principles, among them the ballistic spreading of initially local operators. We have shown, that in certain constrained many-body systems the structure of conservation laws can cause a drastic modification of this universal behavior. As an example, we studied operator growth characterized by out-of-time-order correlations (OTOCs) in a dipole-conserving fracton system. We have identified a critical point with sub-ballistically moving OTOC front, that separates a ballistic from a dynamically frozen phase of operator growth. This critical point is tied to an underlying localization transition and we use its associated scaling properties to derive an effective description of the moving operator front via a biased random walk with long waiting times.
(c) Characterizing exotic phases with constraints
Many-body systems with gauge constraints can lead to unconventional phases of matter with topological order. An example are quantum spin liquids. We have developed a quantum algorithm to realize such states on a superconducting quantum information processor, and have simulated anyon braiding and shown how to measure the topological entanglement entropy of the wave function. We furthermore developed experimental probes of topological phases of matter based on spin-polarized scanning-tunneling microscopy, nitrogen-vacancy center magnetometry, or angle-resolved photoemission spectroscopy. We, moreover, investigated periodically driven quantum spin liquids that are subjected to gauge constraints and identified an unconventional dynamical regime, which cannot be described by a single effective Hamiltonian even in the limit of high driving frequency. The reason for this apparent counter-intuitive behavior is that fractional excitations typically couple asymmetrically to the drive.
With the project ConsQuanDyn, we could shed light on several dynamical phenomena that arise from constraints in quantum many-body systems.
The project ConsQuanDyn has already led to several results which go beyond the state of the art and we will continue to work on our main objectives. Our goal is to ultimately identify a classification of constrained quantum dynamics and propose new experiments to uncover their fundamental principles.